1. Field of the Invention
The present invention relates to an electric potential measuring apparatus capable of measuring an electric potential of an object to be measured (a measurement object) based on the amount of electrical charge induced in a detecting electrode, and an image forming apparatus including the electric potential measuring apparatus, applicable as a copying apparatus, a printer, and the like.
2. Description of the Related Background Art
Conventionally, there exists an image forming apparatus which includes a photosensitive drum and forms an image in an electrophotographic manner. In such an image forming apparatus, the photosensitive drum needs to be uniformly charged in any atmosphere so that a stable image can be obtained at all times. To achieve the above purpose, the charged electric potential of the photosensitive drum is measured by an electric potential measuring apparatus, and a feedback control is executed using the measured result to maintain a uniform electric potential of the photosensitive drum.
As an electric potential measuring apparatus usable for performing the feedback control, there has been developed an electric potential measuring apparatus capable of measuring an electric potential of a measurement object in a non-contacting manner in which any substantial member of the electric potential measuring apparatus is not in contact with a surface of the measurement object.
Description will be given for a potential measuring principle of the electric potential measuring apparatus. Upon generation of an electric field between a surface of a measurement object and a detecting electrode in an electric potential measuring apparatus, charges with an electric amount Q proportional to an electric potential V of the surface of the measurement object are induced in the detecting electrode. The relationship between Q and V is written byQ=CV  (1)where C is the electrostatic capacity (capacitance) between the detecting electrode and the surface of the measurement object. Pursuant to equation (1), the electric potential of the surface of the measurement object can be obtained by measuring the electric amount Q of charges induced in the detecting electrode.
It is, however, difficult to accurately and directly measure the electric amount Q induced in the detecting electrode within a measurement time required by a copying apparatus, a printer, or the like. Accordingly, a practical method is used. In the practical method, the magnitude of the electrostatic capacity C between the detecting electrode and the surface of the measurement object is periodically changed, and the electric potential of the surface of the measurement object is obtained by measuring an AC current signal generated in the detecting electrode by the periodical change.
A principle of obtaining the electric potential of the surface of the measurement object by the above-discussed method will be described. When the electrostatic capacity C is a function of time t, the AC current signal i generated in the detecting electrode can be represented byi=dQ/dt=d(CV)/dt  (2)since the AC current signal i is a value of a time derivative of the electric amount Q induced in the detecting electrode, and the equation (1) holds.
Where a changing speed of the electric potential V of the surface of the measurement object is sufficiently slow relative to a changing speed of the electrostatic capacity C, the equation (2) can be replaced byi=V·dC/dt  (3)since the electric potential V can be assumed to be constant during a short time dt.
From the equation (3), it can be understood that the magnitude of the AC current signal i generated in the detecting electrode is a linear function of the electric potential V of the surface of the measurement object. Therefore, the electric potential of a measurement object can be acquired by measuring the amplitude of an AC current signal.
As a method of periodically changing an electrostatic capacity C between a detecting electrode and a surface of a measurement object, there are typically three methods: (1) a method of periodically changing an effective area of the detecting electrode exposed to the surface of the measurement object, (2) a method of periodically changing a relative dielectric constant between the detecting electrode and the surface of the measurement object, and (3) a method of periodically changing a distance between the detecting electrode and the surface of the measurement object. This is because the electrostatic capacity C is approximated by the following equation (4),C=A·S/x  (4)where A is the proportional constant having connection with a dielectric constant of a material between the detecting electrode and the surface of the measurement object, and the like, S is the area of the detecting electrode, and x is the distance between the detecting electrode and the surface of the measurement object.
In a situation of the above-discussed conventional technology, the photosensitive drum is down-sized and a structure around the photosensitive drum becomes dense. Accordingly, reduction in size and thickness of an electric potential measuring apparatus is also required. In conventional electric potential measuring apparatuses, a space in the electric potential measuring apparatus is occupied almost by assemblage members of a vibrating cantilever, a driving mechanism for vibrating the cantilever, and the like. Therefore, small-sizing of those assemblage members is indispensable for purposes of reducing the size of the electric potential measuring apparatus.
However, when the driving mechanism and the like are reduced in size, the amount of change in the exposed area S of the detecting electrode, or in the distance x between the detecting electrode and the surface of the measurement object inevitably decreases. Here, from the above equations (3) and (4), the magnitude of a current taken out as an output signal from the above-discussed electric potential measuring apparatus is written asi=V·d(A·S/x)/dt  (5)Therefore, when sizes of the driving mechanism and the like are to be decreased, a value of the time derivative in parentheses in the equation (5) becomes small. As a result, the current signal i of the output signal is likely to be affected by noise from outside, and a measurement precision disadvantageously lowers.
Considering those discussed above, a small-sized electric potential measuring apparatus produced using MEMS (micro-electro-mechanical system) techniques has been recently proposed (see U.S. Pat. No. 6,177,800). The MEMS techniques are techniques for fabricating a micro mechanical mechanism or electric device by utilizing semiconductor micro-processing techniques for large-scale integration and the like. By using the MEMS techniques, it is possible to mass-produce micro mechanical mechanisms integrated with electric devices, and the like, and largely reduce the size and cost of an electric potential measuring apparatus.
An advantage of a method of fabricating an electric potential measuring apparatus by the MEMS techniques is as follows. Reduction in the size and cost of an electric potential measuring apparatus can be achieved by fabricating, on a substrate, a small-sized driving mechanism, a detecting electrode, and a signal processing unit for processing a signal generated in the detecting electrode, which are component elements of the electric potential measuring apparatus. Semiconductor with an intentionally-enhanced carrier concentration is often used as the substrate such that electronic circuits for signal-processing and the like can be constructed on the substrate.
It is, however, known that resistivity of the semiconductor with a high carrier concentration is low. Therefore, when a material with a low resistivity is used as the substrate, it is likely that non-negligible stray capacity appears between the substrate, and the detecting electrode and electric wire formed on the substrate through an insulating thin film. Hence, almost all of AC signals generated in the detecting electrode or electric wire flow into another detecting electrode or electric wire through the stray capacity. This phenomenon occurs in all detecting electrodes and electric wires similarly. Therefore, an AC signal in a detecting electrode mixes with a driving signal for driving the driving mechanism, for example. Thus, measurement of an accurate electric potential value is likely to be prevented.
Difficulty of conduction of an AC signal with a frequency f between a detecting electrode or electric wire, and another detecting electrode or electric wire, i.e., an absolute value |Z| of impedance Z therebetween, is given by|Z|={(ar)2+[1/(2πf)·(1/Ch+1/C′h)]2}1/2  (6)where Ch is the stray capacity between a detecting electrode and the substrate, C′h is the stray capacity between another detecting electrode and the substrate, r is the resistivity of the substrate, and a is a proportional constant. It can be understood from the equation (6) that the absolute value |Z| of the impedance Z among detecting electrodes and electric wires should be increased in order to reduce or eliminate mixture of AC signals among detecting electrodes and electric wires. In other words, it is necessary to increase the resistivity r of a portion of the substrate between detecting electrodes, and/or to decrease the stray capacity Ch between the detecting electrode and the substrate.